Subgroups — Q₈×#14268650 #28406987

Order 14464.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14268650	C₂	1	3	yes	maximal
2	C₄×#14268650	C₂	1	3	yes	maximal
3	Q₈×#11744751	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268650	C₂²	1	3	yes	—
5	C₂×#14268650	C₂²	1	1	yes	characteristic
6	C₄⋊#11744751	C₄	1	3	yes	—
7	C₄×#11744751	C₂²	1	3	yes	—
8	C₄×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
9	#14268650	—	2	3	no	—
10	#14268650	Q₈	1	2	yes	direct product factor
11	C₂×#11744751	C₂×C₄	1	3	yes	—
12	C₂×#11744751	C₂³	1	1	yes	characteristic
13	C₂×Q₈×C₁₁₃	C₈	1	1	yes	characteristic
14	C₄⋊C₄×C₁₁₃	C₈	1	3	yes	—
15	C₄²×C₁₁₃	C₂×C₄	1	3	yes	—
16	Q₈×C₁₁₃	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₁₁₃	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₁₁₃	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
20	#11744751	—	2	3	no	—
21	#11744751	C₂×Q₈	1	1	yes	characteristic
22	#11744751	#41	1	1	yes	characteristic
23	C₂²×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₁₁₃	—	2	3	no	—
25	C₄×C₁₁₃	C₂×C₁₆	1	6	yes	—
26	C₄×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₁₁₃	#131	1	1	yes	characteristic
28	C₂×C₁₁₃	C₈×Q₈	1	1	yes	characteristic
29	C₂×C₁₁₃	C₂²×C₁₆	1	1	yes	characteristic
30	C₂×C₁₁₃	#504	1	1	yes	characteristic
31	Q₈×C₁₆	—	113	1	no	maximal, Sylow
32	C₁₁₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₈×Q₈	—	113	1	no	—
34	C₄⋊C₁₆	—	113	3	no	—
35	C₄×C₁₆	—	113	3	no	—
36	C₄×Q₈	#90673	1	1	yes	characteristic
37	C₂×C₁₆	—	113	1	no	—
38	C₂×C₁₆	—	113	3	no	—
39	C₄⋊C₈	—	113	3	no	—
40	C₄×C₈	—	113	3	no	—
41	C₂×Q₈	#11744753	1	1	yes	characteristic
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	113	3	no	—
44	C₄⋊C₄	#11744753	1	3	yes	—
45	C₄²	C₂×#90673	1	3	yes	—
46	C₁₆	—	113	2	no	—
47	C₁₆	—	226	3	no	—
48	Q₈	#14268650	1	4	yes	direct product factor
49	C₂×C₄	C₂×#11744753	1	3	yes	—
50	C₂×C₄	C₂×#11744753	1	3	yes	—
51	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
52	C₈	—	113	1	no	—
53	C₈	—	113	1	no	—
54	C₈	—	226	3	no	—
55	C₂²	C₂²×#11744753	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#14268650	1	6	yes	—
58	C₄	Q₈×#90673	1	1	yes	characteristic
59	C₄	#16813710	1	1	yes	characteristic
60	C₂	Q₈×#11744753	1	1	yes	characteristic
61	C₂	C₂²×#14268650	1	1	yes	characteristic
62	C₂	#20299656	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#90673
commutator	C₂×C₁₁₃	C₂²×C₁₆
Fitting	C₄×Q₈×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	C₂²×C₈
cosocle	C₂×#11744751	C₂³
hypercenter	C₄×Q₈	#90673
hypocenter	C₁₁₃	Q₈×C₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. #14268650	Q₈	direct (N × H)
16. Q₈×C₁₁₃	C₁₆	semidirect
32. C₁₁₃	Q₈×C₁₆	semidirect
48. Q₈	#14268650	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄⋊#14268650	2
C₄×#14268650	2
Q₈×#11744751	2
Q₈×C₁₆	113

Subgroups — Q8×#14268650 #28406987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#14268650 #28406987